A210713 -id:A210713 - cp's OEIS frontend

A198313 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 3.

0, 0, 0, 1, 1, 1, 4, 4, 15, 23, 162, 540, 18958, 389417, 50314520, 2942196930, 1698517018988

Offset: 0

Jason Kimberley, May 24 2012

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g

Not necessarily connected k-regular simple graphs girth exactly 3: this sequence (any k), A185643 (triangle); fixed k: A026796 (k=2), A185133 (k=3), A185143 (k=4), A185153 (k=5), A185163 (k=6).

Not necessarily connected regular simple graphs girth exactly g: this sequence (g=3), A198314 (g=4), A198315 (g=5), A198316 (g=6), A198317 (g=7), A198318 (g=8).

a(n) = A186743(n) + A210713(n).
a(n) = A005176(n) - A185314(n).
a(n) is the sum of the n-th row of A185643.

A185033 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 8, 29, 138, 774, 5678, 53324, 622716, 8604351, 135344959, 2363662004, 45134533117, 933058713014, 20735549517852, 492653820710746

Offset: 0

Jason Kimberley, Feb 29 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: this sequence (k=3), A185043 (k=4), A185053 (k=5), A185063 (k=6).

Disconnected 3-regular simple graphs with girth exactly g: this sequence (g=3), A185034 (g=4), A185035 (g=5), A185036 (g=6), A185037 (g=7).

a(n) = A165653(n) - A185234(n).

A185043 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 8, 25, 88, 377, 2026, 13349, 104593, 930571, 9124627, 96699740, 1095467916, 13175254799, 167460501260, 2241576473025, 31510509517563, 464047467911837, 7143984462730072, 114749034352969037, 1919656978492976231

Offset: 0

Jason Kimberley, Feb 29 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

4-regular simple graphs with girth exactly 3: A184943 (connected), this sequence (disconnected), A185143 (not necessarily connected).
Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), this sequence (k=4), A185053 (k=5), A185063 (k=6).
Disconnected 4-regular simple graphs with girth exactly g: this sequence (g=3), A185044 (g=4).

a(n) = A033483(n) - A185244(n).

Terms a(27)-a(31), due to the extension of A006820 by Andrew Howroyd, from Jason Kimberley, Mar 16 2020

A185053 Number of disconnected 5-regular simple graphs on 2n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 3, 66, 8029, 3484759, 2595985769, 2815099031409

Offset: 0

Jason Kimberley, Mar 10 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), A185043 (k=4), this sequence (k=5), A185063 (k=6).

a(n) = A165655(n) - A185254(n).

A210703 Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 0, 3, 0, 1, 0, 0, 4, 8, 3, 1, 0, 0, 5, 0, 8, 0, 0, 0, 6, 29, 25, 3, 1, 0, 0, 9, 0, 88, 0, 1, 0, 0, 10, 138, 377, 66, 5, 1, 0, 0, 13, 0, 2026, 0, 25, 0, 0, 0, 17, 774, 13349, 8029, 297, 5, 1, 0, 0, 21, 0, 104593, 0, 8199, 0, 1, 0, 0, 25, 5678, 930571, 3484759, 377004, 1562, 7, 1

Offset: 2

Jason Kimberley, Jan 21 2013

			2: 0;
3: 0;
4: 0, 0;
5: 0, 0;
6: 0, 0, 1;
7: 0, 0, 1;
8: 0, 0, 1, 1;
9: 0, 0, 2, 0;
10: 0, 0, 2, 2, 1;
11: 0, 0, 3, 0, 1;
12: 0, 0, 4, 8, 3, 1;
13: 0, 0, 5, 0, 8, 0;
14: 0, 0, 6, 29, 25, 3, 1;
15: 0, 0, 9, 0, 88, 0, 1;
16: 0, 0, 10, 138, 377, 66, 5, 1;
17: 0, 0, 13, 0, 2026, 0, 25, 0;
18: 0, 0, 17, 774, 13349, 8029, 297, 5, 1;
19: 0, 0, 21, 0, 104593, 0, 8199, 0, 1;
20: 0, 0, 25, 5678, 930571, 3484759, 377004, 1562, 7, 1;
21: 0, 0, 33, 0, 9124627, 0, 22014143, 0, 100, 0;
22: 0, 0, 39, 53324, 96699740, 2595985769, 1493574756, 21617036, 10901, 9, 1;
23: 0, 0, 49, 0, 1095467916, 0, 114880777582, 0, 3470736, 0, 1;
24: 0, 0, 60, 622716, 13175254799, 2815099031409, 9919463450854, 733460349818, 1473822243, 88238, 11, 1;

Jason Kimberley, Table of i, a(i)=D(n,k) for i = 2..145 (n = 2..24)
Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

The sum of the n-th row is A210713(n).

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), this sequence (triangle); for a fixed k: A185033 (k=3), A185043 (k=4), A185053 (k=5), A185063 (k=6).

D(n,k) = A068933(n,k) - A185204(n,k) [the former is padded to be a tabl but the latter is a tabf].

D(n,k) = A185643(n,k) - A186733(n,k) [both are tabl but the result is tabf].

A185063 Number of disconnected 6-regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 25, 297, 8199, 377004, 22014143, 1493574756, 114880777582, 9919463450854

Offset: 0

Jason Kimberley, Mar 10 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), A185043 (k=4), A185053 (k=5), this sequence (k=6).

a(n) = A165656(n) - A185264(n).

cp's OEIS Frontend

A198313 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 3.

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A185033 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 3.

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A185043 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 3.

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A185053 Number of disconnected 5-regular simple graphs on 2n vertices with girth exactly 3.

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A210703 Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth exactly 3.

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A185063 Number of disconnected 6-regular simple graphs on n vertices with girth exactly 3.

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